Cardiac output estimation using ballistocardiography: a feasibility study in healthy subjects

There is no reliable automated non-invasive solution for monitoring circulation and guiding treatment in prehospital emergency medicine. Cardiac output (CO) monitoring might provide a solution, but CO monitors are not feasible/practical in the prehospital setting. Non-invasive ballistocardiography (BCG) measures heart contractility and tracks CO changes. This study analyzed the feasibility of estimating CO using morphological features extracted from BCG signals. In 20 healthy subjects ECG, carotid/abdominal BCG, and invasive arterial blood pressure based CO were recorded. BCG signals were adaptively processed to isolate the circulatory component from carotid (CCc) and abdominal (CCa) BCG. Then, 66 features were computed on a beat-to-beat basis to characterize amplitude/duration/area/length of the fluctuation in CCc and CCa. Subjects’ data were split into development set (75%) to select the best feature subset with which to build a machine learning model to estimate CO and validation set (25%) to evaluate model’s performance. The model showed a mean absolute error, percentage error and 95% limits of agreement of 0.83 L/min, 30.2% and − 2.18–1.89 L/min respectively in the validation set. BCG showed potential to reliably estimate/track CO. This method is a promising first step towards an automated, non-invasive and reliable CO estimator that may be tested in prehospital emergencies.


Supplementary materials
Invasive procedure and safety The invasive procedure conducted in the study consisted in the insertion of a radial arterial line catheter.This procedure was necessary for using the pulse contour waveform technology that measures the blood pressures to calculate stroke volume and cardiac output when doppler echocardiography was impossible to do.There was a need of a technology that can be used out of hospital in emergency medicine cases where doppler echocardiography is impossible to use.
To perform the invasive procedure, volunteers were met and taken care of by a dedicated safety nurse when arriving at the hospital and throughout of the study.The safety nurse put on EMLA cream (topical anaesthetic) on the skin over the radial artery 30 minutes before canulation.A consultant in anesthesiology using an ultrasound (US) image inserted an arterial line catheter according to the hospital's standard for arterial access to the artery under sterile conditions for each volunteer at the pre-operative area (entrance to the operating theater).After the artery lumen was "hit" (verified by US visualization and backflow of blood in the needle) but not penetrated, the catheter was flushed and secured.The volunteer waited 15 minutes to verify no side effects before followed by the safety nurse to the study area in the cardiology department.Trained personnel connected HemoSphere FloTrac blood pressure sensor (Edwards Lifesciences Corporation, Nyon, Switzerland) to the artery line for continuous monitoring.The volunteers were informed to verbally report any discomforts.After each volunteer had been through the study protocol the arterial line was removed by applying pressure to the insertion site for 10 minutes while observed for bleeding or discomforts and a pressure bandage was applied.Volunteers were followed up concerning pain or discomfort for 30 minutes.All volunteers could call a mobile phone number 24/7 if they had any concerns or questions after the study day.

Adaptive extraction of the circulatory component
Healthy subjects present a pulse so that the ballistocardiogram (BCG) signal, s bcg (n), can be expressed using the following additive model: where sample index n is related to time by t = n/f s , with a sampling frequency of f s = 250 Hz. s rest (n) contains the BCG baseline value and artifacts mostly due to sensor movement and skin-sensor contact.Each effective contraction of the heart ejects blood into the aorta and produces fluctuations in the BCG, that is the circulatory-related component, CC(n).Consecutive fluctuations slightly vary in amplitude and duration.Hence, CC(n) presents a quasi-periodic nature and can be modeled using a Fourier series with N terms of slowly time-varying amplitudes and frequencies: where N represents the number of harmonics.The Fourier coefficients a k (n) and b k (n) represent the in-phase and quadrature amplitudes of the model, and ω 0 (n) = 2πf 0 (n)/f s its fundamental frequency.The sample indices of the R peaks of the QRS complexes, r i , were detected using the Hamilton-Tompkins algorithm [1,2] and used to compute f 0 (n) as follows: where f 0 (n) is constant within each QRS interval, but varies for consecutive intervals.
The estimation of a k (n) and b k (n) was carried out through the Recursive Least Squares (RLS) adaptive algorithm [3,4,5].The RLS algorithm was used with the classical configuration for adaptive interference canceling proposed by Widrow et al. [6] illustrated in Figure 2.
are the so-called reference signal (harmonics) and weight vector (coefficients), respectively.The RLS algorithm searches for the w(n) that minimizes the following cost function that represents a weighted squared error where the error, e(n), is the difference between the desired signal, d(n) = s bcg (n), and the estimated circulatory component, CC(n): and λ is the so-called forgetting factor that governs the convergence rate and stability of the RLS algorithm.A small λ speeds up the convergence rate at the risk of turning the process unstable [4,5,7].The minimization of C(n) results in the following update equations for the w(n): where the gain matrix F(n) and the weight vector are initialized to F(0) = 0.03I 2N and w(0) = 0 T with I 2N representing the identity matrix of order 2N .
The optimization of the configuration of the RLS algorithm consists in tuning two parameters N and λ.In this study, N = 4 and λ = 0.9993 were selected based on our previous experiences extracting circulatory-related components [3,7] and optimization results obtained using the development set.

Feature extraction
A total of 66 waveform features were computed to characterize the amplitude, duration, area and length of the fluctuations for each 10-s analysis window of the carotid, CC c (n), and abdominal, CC a (n), circulatory components.Specifically, 33 features were calculated from each circulatory component.The first three features were the standard deviation, skewness and kurtosis of the circulatory component aiming to describe its statistical distribution.The last 30 features corresponded to the median and standard deviation of the following 15 morphological characteristics were computed on a beat-to-beat basis: 1. Peak amplitude (a M ): the amplitude of the highest peak in the fluctuation as shown in Fig. 2.
2. Onset-peak amplitude (A 1 ): the peak-to-trough amplitude from onset to peak of the fluctuation (see Fig. 3).3. Offset-peak amplitude (A 2 ): the peak-to-trough amplitude from offset to peak of the fluctuation (see Fig. 4).4. Maximum amplitude (A max ): the maximum amplitude between A 1 and A 2 .

5.
Mean amplitude (A mean ): the mean value of amplitudes A 1 and A 2 .
6. Onset-peak duration (D 1 ): the duration from the onset to the peak of the fluctuation as illustrated in Fig. 5. 7. Peak-offset duration (D 2 ): the duration from the peak to the offset of the fluctuation as shown in Fig. 6.
8. Total duration (D t ): the duration from the onset to the offset of the fluctuation (see Fig. 7).9. Pulse width (P w ): the duration of the upper half of fluctuation (see Fig. 8).10.Onset-peak area (Ar 1 ): the area from the onset to the peak of the fluctuation as illustrated in Fig. 9 where T s = 1/f s represents the sampling period, the inverse of the sampling frequency, f s .11. Peak-offset area (Ar 2 ): the area from the peak to the offset of the fluctuation as shown in Fig. 10.12.Total area (Ar t ): the area from the onset to the offset of the fluctuation (see Fig. 11).13.Onset-peak length (L 1 ): the curve length from the onset to the peak of the fluctuation as illustrated in Fig. 12.
14. Peak-offset length (L 2 ): the curve length from the peak to the offset of the fluctuation as shown in Fig. 13. 15.Total length (L t ): the curve length from the onset to the offset of the fluctuation (see Fig. 14).

Multiple linear regression model
All the details of the final multiple linear regression model are shown in Table 1.

Additional results
Figure 15 shows boxplots representing the evolution of the absolute error across the different phases of the study protocol for development (top panels) and validation (bottom panel) sets, respectively.

Figure 1 .
Figure 1.Block diagram of the RLS adaptive filter used to extract the circulatory component, CC(n).

Figure 2 .
Figure 2. Bland-Altman plots for each phase in the development (top) and validation (bottom) sets.

Table 1 .
Details of the adjusted multiple linear regression model.
Abbreviations: SE standard error, CI confidence interval.